We present an approach to the uniformization of certain Shimura curves by means of automorphic functions, obtained by integration of non-linear differential equations. The method takes as its starting point a differential construction of the modular j-function, first worked out by R. Dedekind in 1877, and makes use of a differential operator of the third order, introduced by H. A. Schwarz in 1873.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-1,
author = {Pilar Bayer},
title = {Uniformization of certain Shimura curves},
journal = {Banach Center Publications},
volume = {58},
year = {2002},
pages = {13-26},
zbl = {1036.11026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-1}
}
Pilar Bayer. Uniformization of certain Shimura curves. Banach Center Publications, Tome 58 (2002) pp. 13-26. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-1/